Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
441 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 441 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×Q8×C25 | C2 | semidirect |
| 3. Q8×Dic25 | C2 | semidirect |
| 4. #11716455 | C2 | semidirect |
| 5. C4⋊C4×D25 | C2 | semidirect |
| 6. C4×D100 | C2 | semidirect |
| 7. #11716434 | C2 | semidirect |
| 9. #87748 | C4 | semidirect |
| 23. Q8×C25 | C2×C4 | semidirect |
| 30. D100 | C2×C4 | semidirect |
| 32. C4×D25 | C2×C4 | semidirect |
| 81. C4×Q8 | D25 | semidirect |
| 86. C25 | #520 | semidirect |
| 115. Q8 | C4×D25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87748 | 2 |
| C4×Q8×C25 | 2 |
| Q8×Dic25 | 2 |
| #11716455 | 2 |
| C4⋊C4×D25 | 2 |
| C4×D100 | 2 |
| #11716434 | 2 |
| #65908 | 5 |